Differential Eq...

The general solution of $$xy^{5}=y_{4}(y_{n}=\displaystyle\frac{d^{n}y}{dx^{n}})$$ is given by:

$$\displaystyle \frac {dy}{dx}\, +\, \sin\, \displaystyle \frac {x+y}{2}\, =\, \sin\, \displaystyle \frac {x-y}{2}$$

$$\displaystyle \frac {dy}{dx}\, =\, \displaystyle \frac {x(2\ln\, x\, +\, 1)}{\sin\, y\, +\, y\cos\, y}$$

The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact is:

If $$y=\sin ^{ -1 }{ \left[ \sqrt { x-ax } -\sqrt { a-ax }  \right]  } $$, then $$\cfrac { dy }{ dx } $$ is equal to

The solution of $$\cfrac { dy }{ dx } ={ 2 }^{ y-x }$$ is

A curve, whose concavity is directly proportional to the logarithm of its x-coordinate at any point of curve, is given by:

The order of the differential equation whose solution is $$y=a\cos { x } +b\sin { x } +c{ e }^{ -x }$$, is

$$\cfrac { d }{ dx } \left[ \tan ^{ -1 }{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -1 }{ x }  }  \right] $$ is equal to